Polya's 4 Steps of Problem Solving

1. Understand the problem.
   • Understand the situation.
   • Draw a diagram/picture if needed.
   • What is known? What is unknown?
   • What is the question?
   • How do various quantities in the problem relate?
2. Devise a Plan.
   • Think of a strategy that can be used to solve the problem.
3. Carry Out the Plan.
   • Attempt to solve the problem with the chosen strategy.
   • If the strategy does not work, return to step 2 (try another strategy).
4. Looking Back.
   • Check your answer, if possible. (In particular, solve the problem in a different way, if possible.)
   • Does your answer make sense?
   • Is there a way to simplify your solution?
   • Is there a way to simplify the presentation of your solution? (Note: depending on your audience, "simplify" might mean different things.)
   • Are there any other (perhaps simpler) approaches?
   • If you did not use a diagram/picture, would one help you to explain your solution?

Strategies for Problem Solving (for step 2)

• Draw a diagram
• Make a table
• Look for a Pattern
• Examine a simpler problem (e.g. for smaller numbers)
• Examine a special case
• Examine all cases
• Break the problem into smaller/simplier pieces
• Identify a subgoal
• Examine a related problem
• Work backwards
• Write an equation or a system of equations
• Use indirect reasoning
• Use related theorems
• Guess and check